Real positive number/Root/Unique existence/Fact

Existence of real roots

For every nonnegative real number ${}c\in \mathbb {R} _{\geq 0}$ and every ${}k\in \mathbb {N} _{+}$

there exists a unique nonnegative real number ${}x$ fulfilling

${}x^{k}=c\,.$

Proof, Write another proof